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\title{Generalization Error}
\author{ML Instruction Team, Fall 2022}
\institute[]{CE Department \newline  Sharif University of Technology \newline \newline}
\date[\today]{}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Title Page Info %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Begin Your Document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
	
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	\fontsize{9}{9}
\begin{frame}[noframenumbering, plain]
	\titlepage
\end{frame}

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\section{Validation }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame{\frametitle{Why Evaluation?}
\begin{itemize}
\item Estimation of the generalization error\smallskip
\item  Increasing of the predictive performance \smallskip
\item Selecting best-suited  ML algorithm for our problem
\end{itemize}

}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame{\frametitle{Why Validation?}
\begin{itemize}
\item Training set error is an optimistically biased estimator of the generalization error\smallskip
\item  Test set error is an unbiased estimator of the generalization error \smallskip
\end{itemize}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######
\frame{\frametitle{ Validation }
\begin{figure}
				\href{https://pdfs.semanticscholar.org/d376/6b9cbf69cab9343e25a817d824f84983b1f9.pdf}{
				\centering
				\includegraphics[width=10cm]{images/Validation.jpg}}
\end{figure}

	
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######
\frame{\frametitle{Types of Validation}

\begin{itemize}
\item Holdout Validation\smallskip
\item LOOCV (Leave One Out Cross Validation)\smallskip
\item K-Fold Cross Validation\smallskip
\end{itemize}

}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######
\frame{\frametitle{ Holdout Validation}

\begin{figure}
				\href{https://algotrading101.com/learn/train-test-split}{
				\centering
				\includegraphics[width=8cm]{images/Holdout Validation.png}}
\end{figure}
\begin{itemize}
\item Pros \begin{itemize}
\item Fully independent of data
\item Lower computational costs
\end{itemize}
\item Cons \begin{itemize}
\item higher variance
\end{itemize}
\end{itemize}


}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######
\frame{\frametitle{LOOCV}

\begin{figure}
				\href{https://medium.datadriveninvestor.com/leave-one-out-cross-validation-32fa248c1739}{
				\centering
				\includegraphics[width=8cm,height=4cm]{images/loocv2.png}}
\end{figure}
\begin{itemize}
\item Pros \begin{itemize}
\item Lower bias
\end{itemize}
\item Cons \begin{itemize}
\item Higher computational cost
\end{itemize}
\end{itemize}


}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######
\frame{\frametitle{K-Fold Cross Validation}

\begin{figure}
				\href{https://towardsdatascience.com/cross-validation-c4fae714f1c5}{
				\centering
				\includegraphics[width=9cm, height=4cm]{images/K-Fold Cross Validation.png}}
\end{figure}
\begin{itemize}
\item Pros \begin{itemize}
\item Lower computational compared to LOOCV
\item Lower variance campared to Holdout
\item Reducing both Bias and Variance
\end{itemize}	
\item Cons \begin{itemize}
\item Higher computational costs in big data state
\item Impact model in imbalanced data state
\end{itemize}
\end{itemize}


}

\section{Model Selection}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######
\frame{\frametitle{Hyperparameter Tuning}
}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######


\frametitle{Final Notes}
\centering
\vspace{50 pt}
\textbf{Thank You!}

\vspace{50pt}
\textbf{Any Question?}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}
